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<div class="title">core_theorem_producer.cpp</div> </div>
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<a href="core__theorem__producer_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">/*****************************************************************************/</span><span class="comment"></span>
<a name="l00002"></a>00002 <span class="comment">/*!</span>
<a name="l00003"></a>00003 <span class="comment"> * \file core_theorem_producer.cpp</span>
<a name="l00004"></a>00004 <span class="comment"> * </span>
<a name="l00005"></a>00005 <span class="comment"> * Author: Sergey Berezin</span>
<a name="l00006"></a>00006 <span class="comment"> * </span>
<a name="l00007"></a>00007 <span class="comment"> * Created: Feb 05 03:40:36 GMT 2003</span>
<a name="l00008"></a>00008 <span class="comment"> *</span>
<a name="l00009"></a>00009 <span class="comment"> * <hr></span>
<a name="l00010"></a>00010 <span class="comment"> *</span>
<a name="l00011"></a>00011 <span class="comment"> * License to use, copy, modify, sell and/or distribute this software</span>
<a name="l00012"></a>00012 <span class="comment"> * and its documentation for any purpose is hereby granted without</span>
<a name="l00013"></a>00013 <span class="comment"> * royalty, subject to the terms and conditions defined in the \ref</span>
<a name="l00014"></a>00014 <span class="comment"> * LICENSE file provided with this distribution.</span>
<a name="l00015"></a>00015 <span class="comment"> * </span>
<a name="l00016"></a>00016 <span class="comment"> * <hr></span>
<a name="l00017"></a>00017 <span class="comment"> * </span>
<a name="l00018"></a>00018 <span class="comment"> */</span>
<a name="l00019"></a>00019 <span class="comment">/*****************************************************************************/</span>
<a name="l00020"></a>00020 <span class="comment">// CLASS: CoreTheoremProducer</span>
<a name="l00021"></a>00021 <span class="comment">//</span>
<a name="l00022"></a>00022 <span class="comment">// AUTHOR: Sergey Berezin, 12/09/2002</span>
<a name="l00023"></a>00023 <span class="comment">// Vijay Ganesh, september 15th, 2004 (CNF Converter rules)</span>
<a name="l00024"></a>00024 <span class="comment">//</span>
<a name="l00025"></a>00025 <span class="comment">// Description: Implementation of the proof rules for ground</span>
<a name="l00026"></a>00026 <span class="comment">// equational logic (reflexivity, symmetry, transitivity, and</span>
<a name="l00027"></a>00027 <span class="comment">// substitutivity).</span>
<a name="l00028"></a>00028 <span class="comment">//</span><span class="comment"></span>
<a name="l00029"></a>00029 <span class="comment">///////////////////////////////////////////////////////////////////////////////</span>
<a name="l00030"></a>00030 <span class="comment"></span>
<a name="l00031"></a>00031
<a name="l00032"></a>00032 <span class="comment">// This code is trusted</span>
<a name="l00033"></a><a class="code" href="core__theorem__producer_8cpp.html#a8663c36bbf15bb5a0dcb01b97897fa95">00033</a> <span class="preprocessor">#define _CVC3_TRUSTED_</span>
<a name="l00034"></a>00034 <span class="preprocessor"></span>
<a name="l00035"></a>00035
<a name="l00036"></a>00036 <span class="preprocessor">#include "<a class="code" href="core__theorem__producer_8h.html">core_theorem_producer.h</a>"</span>
<a name="l00037"></a>00037 <span class="preprocessor">#include "<a class="code" href="theory__core_8h.html">theory_core.h</a>"</span>
<a name="l00038"></a>00038
<a name="l00039"></a>00039
<a name="l00040"></a>00040 <span class="keyword">using namespace </span>CVC3;
<a name="l00041"></a>00041 <span class="keyword">using namespace </span>std;
<a name="l00042"></a>00042
<a name="l00043"></a>00043
<a name="l00044"></a>00044 <span class="comment">// The trusted method of TheoryCore which creates this theorem producer</span>
<a name="l00045"></a><a class="code" href="classCVC3_1_1TheoryCore.html#a5b386f16781365b7421e884baaebae41">00045</a> <a class="code" href="classCVC3_1_1CoreProofRules.html">CoreProofRules</a>* <a class="code" href="classCVC3_1_1TheoryCore.html#a5b386f16781365b7421e884baaebae41" title="Private method to get a new theorem producer.">TheoryCore::createProofRules</a>(<a class="code" href="classCVC3_1_1TheoremManager.html">TheoremManager</a>* tm) {
<a name="l00046"></a>00046 <span class="keywordflow">return</span> <span class="keyword">new</span> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html">CoreTheoremProducer</a>(tm, <span class="keyword">this</span>);
<a name="l00047"></a>00047 }
<a name="l00048"></a>00048
<a name="l00049"></a>00049
<a name="l00050"></a>00050 <span class="comment">// e: T ==> |- typePred_T(e) [asserting the type predicate of e]</span>
<a name="l00051"></a>00051 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00052"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a0b6d312ded517ab466308ec5981d250e">00052</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a0b6d312ded517ab466308ec5981d250e" title="e: T ==> |- typePred_T(e) [deriving the type predicate of e]">CoreTheoremProducer::typePred</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l00053"></a>00053 <a class="code" href="classCVC3_1_1Type.html" title="MS C++ specific settings.">Type</a> tp(e.<a class="code" href="group__ExprPkg.html#ga42929221eb172250697b72c28af6de07" title="Get the type. Recursively compute if necessary.">getType</a>());
<a name="l00054"></a>00054 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> pred(d_core->getTypePred(tp, e));
<a name="l00055"></a>00055 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00056"></a>00056 <span class="keywordflow">if</span>(withProof()) {
<a name="l00057"></a>00057 pf = newPf(<span class="stringliteral">"type_pred"</span>, e, tp.getExpr());
<a name="l00058"></a>00058 }
<a name="l00059"></a>00059 <span class="keywordflow">return</span> newTheorem(pred, <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00060"></a>00060 }
<a name="l00061"></a>00061
<a name="l00062"></a>00062
<a name="l00063"></a>00063 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00064"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a222db72dc6f637e582dfb9b8dd4e362c">00064</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a222db72dc6f637e582dfb9b8dd4e362c" title="Replace LETDECL with its definition.">CoreTheoremProducer::rewriteLetDecl</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l00065"></a>00065 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00066"></a>00066 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5ba9508dd8c8e7db280a5dacc19bd74d92d">LETDECL</a>,
<a name="l00067"></a>00067 <span class="stringliteral">"rewriteLetDecl: wrong expression: "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00068"></a>00068 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00069"></a>00069 <span class="keywordflow">if</span>(withProof()) <span class="comment">// FIXME: implement this in flea</span>
<a name="l00070"></a>00070 pf = newPf(<span class="stringliteral">"rewrite_letdecl"</span>, e[1]);
<a name="l00071"></a>00071 <span class="keywordflow">return</span> newRWTheorem(e, e[1], <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00072"></a>00072 }
<a name="l00073"></a>00073
<a name="l00074"></a>00074 <span class="comment">// ==> NOT (AND e1 ... en) IFF (OR !e1 ... !en), takes (AND ...)</span>
<a name="l00075"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a66f5d185eca0ccf417b4bf5ed4448f72">00075</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a66f5d185eca0ccf417b4bf5ed4448f72" title="==> NOT (AND e1 ... en) IFF (OR !e1 ... !en), takes (AND ...)">CoreTheoremProducer::rewriteNotAnd</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l00076"></a>00076 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00077"></a>00077 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#ga1a898858ccadce833df5a294c7740f11">isNot</a>() && e[0].<a class="code" href="group__ExprPkg.html#ga383260cf4f8919728e2712e6e11f21fa">isAnd</a>(),
<a name="l00078"></a>00078 <span class="stringliteral">"rewriteNotAnd: precondition violated: "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00079"></a>00079
<a name="l00080"></a>00080
<a name="l00081"></a>00081 vector<Expr> kids; <span class="comment">// vector of <!e1,...,!en></span>
<a name="l00082"></a>00082 <span class="keywordflow">for</span>(<a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i=e[0].begin(), iend=e[0].<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); i!=iend; ++i)
<a name="l00083"></a>00083 <span class="comment">// Collapse double negations</span>
<a name="l00084"></a>00084 kids.push_back(i->negate());
<a name="l00085"></a>00085 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00086"></a>00086 <span class="keywordflow">if</span>(withProof())
<a name="l00087"></a>00087 pf = newPf(<span class="stringliteral">"rewrite_not_and"</span>, e);
<a name="l00088"></a>00088 <span class="keywordflow">return</span> newRWTheorem(e, <a class="code" href="namespaceCVC3.html#a30f30b6e20c174f21ae63acea8618294">orExpr</a>(kids), <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00089"></a>00089 }
<a name="l00090"></a>00090
<a name="l00091"></a>00091 <span class="comment">// ==> NOT (OR e1 ... en) IFF (AND !e1 ... !en), takes (OR ...)</span>
<a name="l00092"></a>00092 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00093"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a5ce6abeb6a346d20f5d5860a30a33e28">00093</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a5ce6abeb6a346d20f5d5860a30a33e28" title="==> NOT (OR e1 ... en) IFF (AND !e1 ... !en), takes (OR ...)">CoreTheoremProducer::rewriteNotOr</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l00094"></a>00094 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00095"></a>00095 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#ga1a898858ccadce833df5a294c7740f11">isNot</a>() && e[0].<a class="code" href="group__ExprPkg.html#ga36f1eff876808586db368dc1b6da5f56">isOr</a>(),
<a name="l00096"></a>00096 <span class="stringliteral">"rewriteNotOr: precondition violated: "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00097"></a>00097 vector<Expr> kids; <span class="comment">// vector of <!e1,...,!en></span>
<a name="l00098"></a>00098 <span class="keywordflow">for</span>(<a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i=e[0].begin(), iend=e[0].<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); i!=iend; ++i)
<a name="l00099"></a>00099 <span class="comment">// Collapse double negations</span>
<a name="l00100"></a>00100 kids.push_back(i->negate());
<a name="l00101"></a>00101 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00102"></a>00102 <span class="keywordflow">if</span>(withProof())
<a name="l00103"></a>00103 pf = newPf(<span class="stringliteral">"rewrite_not_or"</span>, e);
<a name="l00104"></a>00104 <span class="keywordflow">return</span> newRWTheorem(e, <a class="code" href="namespaceCVC3.html#ad4258158bba138eb54b9080af7f8223a">andExpr</a>(kids), <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00105"></a>00105 }
<a name="l00106"></a>00106
<a name="l00107"></a>00107
<a name="l00108"></a>00108 <span class="comment">// ==> NOT IFF(e1,e2) IFF IFF(e1,NOT e2)</span>
<a name="l00109"></a>00109 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00110"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a7da16f5874fbc0870f57a9deeeec80b8">00110</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a7da16f5874fbc0870f57a9deeeec80b8" title="==> NOT IFF(e1,e2) IFF IFF(e1,NOT e2)">CoreTheoremProducer::rewriteNotIff</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l00111"></a>00111 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00112"></a>00112 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00113"></a>00113 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#ga1a898858ccadce833df5a294c7740f11">isNot</a>() && e[0].<a class="code" href="group__ExprPkg.html#gabe385fb97505cccb75702378511c5375">isIff</a>(), <span class="stringliteral">"rewriteNotIff precondition violated"</span>);
<a name="l00114"></a>00114 <span class="keywordflow">if</span>(withProof()) {
<a name="l00115"></a>00115 pf = newPf(<span class="stringliteral">"rewrite_not_iff"</span>, e);
<a name="l00116"></a>00116 }
<a name="l00117"></a>00117 <span class="keywordflow">return</span> newRWTheorem(e, e[0][0].iffExpr(!e[0][1]), <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00118"></a>00118 }
<a name="l00119"></a>00119
<a name="l00120"></a>00120
<a name="l00121"></a>00121 <span class="comment">// ==> NOT ITE(a,b,c) IFF ITE(a,NOT b,NOT c)</span>
<a name="l00122"></a>00122 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00123"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#accd799779aa02c5d84352cc48e975b3d">00123</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#accd799779aa02c5d84352cc48e975b3d" title="==> NOT ITE(a,b,c) IFF ITE(a,NOT b,NOT c)">CoreTheoremProducer::rewriteNotIte</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l00124"></a>00124 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00125"></a>00125 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00126"></a>00126 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#ga1a898858ccadce833df5a294c7740f11">isNot</a>() && e[0].<a class="code" href="group__ExprPkg.html#gaef13fa4752a1fb28e129a1efd0e26f01">isITE</a>(), <span class="stringliteral">"rewriteNotIte precondition violated"</span>);
<a name="l00127"></a>00127 <span class="keywordflow">if</span>(withProof()) {
<a name="l00128"></a>00128 pf = newPf(<span class="stringliteral">"rewrite_not_ite"</span>, e);
<a name="l00129"></a>00129 }
<a name="l00130"></a>00130 <span class="keywordflow">return</span> newRWTheorem(e, e[0][0].iteExpr(!e[0][1], !e[0][2]), <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00131"></a>00131 }
<a name="l00132"></a>00132
<a name="l00133"></a>00133
<a name="l00134"></a>00134 <span class="comment">// a |- b == d ==> ITE(a, b, c) == ITE(a, d, c)</span>
<a name="l00135"></a>00135 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00136"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a490808acd89e0732678d570599c93165">00136</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a490808acd89e0732678d570599c93165" title="a |- b == d ==> ITE(a, b, c) == ITE(a, d, c)">CoreTheoremProducer::rewriteIteThen</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thenThm) {
<a name="l00137"></a>00137 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00138"></a>00138 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l00139"></a>00139 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(withAssumptions(), <span class="stringliteral">"Cannot check proof without assumptions"</span>);
<a name="l00140"></a>00140 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#gaef13fa4752a1fb28e129a1efd0e26f01">isITE</a>() && thenThm.<a class="code" href="classCVC3_1_1Theorem.html#a362c1d70e03803d804bbe300e5f6dc87">isRewrite</a>() && e[1] == thenThm.<a class="code" href="classCVC3_1_1Theorem.html#a206c04f39fbbcacef2337148675553f4">getLHS</a>(),
<a name="l00141"></a>00141 <span class="stringliteral">"rewriteIteThen precondition violated \n then expression: "</span>
<a name="l00142"></a>00142 + thenThm.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>().<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>() + <span class="stringliteral">"\n e = "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00143"></a>00143 }
<a name="l00144"></a>00144 <a class="code" href="classCVC3_1_1Assumptions.html">Assumptions</a> a = thenThm.<a class="code" href="classCVC3_1_1Theorem.html#a5e9ab00a613df15cc02f55edb55a67b3">getAssumptionsRef</a>() - e[0];
<a name="l00145"></a>00145 <span class="keywordflow">if</span>(withProof()) {
<a name="l00146"></a>00146 <a class="code" href="classCVC3_1_1Type.html" title="MS C++ specific settings.">Type</a> t = e.<a class="code" href="group__ExprPkg.html#ga42929221eb172250697b72c28af6de07" title="Get the type. Recursively compute if necessary.">getType</a>();
<a name="l00147"></a>00147 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(!t.<a class="code" href="classCVC3_1_1Type.html#ab5fe00c99ee91f369e3339b26bab0bf7">isNull</a>(), <span class="stringliteral">"rewriteIteThen: e has no type: "</span>
<a name="l00148"></a>00148 + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00149"></a>00149 <span class="keywordtype">bool</span> useIff = t.<a class="code" href="classCVC3_1_1Type.html#a38bba404056eadf3c283a67ab2347e02">isBool</a>();
<a name="l00150"></a>00150 <span class="keywordflow">if</span>(useIff)
<a name="l00151"></a>00151 pf = newPf(<span class="stringliteral">"rewrite_ite_then_iff"</span>, e, thenThm.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l00152"></a>00152 <span class="keywordflow">else</span> {
<a name="l00153"></a>00153 pf = newPf(<span class="stringliteral">"rewrite_ite_then"</span>, e, thenThm.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l00154"></a>00154 }
<a name="l00155"></a>00155 }
<a name="l00156"></a>00156 <span class="keywordflow">return</span> newRWTheorem(e, e[0].iteExpr(thenThm.<a class="code" href="classCVC3_1_1Theorem.html#a97d957fcbf9094480851b1d2e5d3729f">getRHS</a>(), e[2]), a, pf);
<a name="l00157"></a>00157 }
<a name="l00158"></a>00158
<a name="l00159"></a>00159 <span class="comment">// !a |- c == d ==> ITE(a, b, c) == ITE(a, b, d)</span>
<a name="l00160"></a>00160 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00161"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#ae1092dc92aef4300caf926b48ac2ec65">00161</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#ae1092dc92aef4300caf926b48ac2ec65" title="!a |- c == d ==> ITE(a, b, c) == ITE(a, b, d)">CoreTheoremProducer::rewriteIteElse</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& elseThm) {
<a name="l00162"></a>00162 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00163"></a>00163 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l00164"></a>00164 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(withAssumptions(), <span class="stringliteral">"Cannot check proof without assumptions"</span>);
<a name="l00165"></a>00165 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#gaef13fa4752a1fb28e129a1efd0e26f01">isITE</a>() && elseThm.<a class="code" href="classCVC3_1_1Theorem.html#a362c1d70e03803d804bbe300e5f6dc87">isRewrite</a>() && e[2] == elseThm.<a class="code" href="classCVC3_1_1Theorem.html#a206c04f39fbbcacef2337148675553f4">getLHS</a>(),
<a name="l00166"></a>00166 <span class="stringliteral">"rewriteIteElse precondition violated \n else expression: "</span>
<a name="l00167"></a>00167 + elseThm.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>().<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>() + <span class="stringliteral">"\n e = "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00168"></a>00168 }
<a name="l00169"></a>00169 <a class="code" href="classCVC3_1_1Assumptions.html">Assumptions</a> a = elseThm.<a class="code" href="classCVC3_1_1Theorem.html#a5e9ab00a613df15cc02f55edb55a67b3">getAssumptionsRef</a>() - !e[0];
<a name="l00170"></a>00170 <span class="keywordflow">if</span>(withProof()) {
<a name="l00171"></a>00171 <a class="code" href="classCVC3_1_1Type.html" title="MS C++ specific settings.">Type</a> t = e.<a class="code" href="group__ExprPkg.html#ga42929221eb172250697b72c28af6de07" title="Get the type. Recursively compute if necessary.">getType</a>();
<a name="l00172"></a>00172 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(!t.<a class="code" href="classCVC3_1_1Type.html#ab5fe00c99ee91f369e3339b26bab0bf7">isNull</a>(), <span class="stringliteral">"rewriteIteElse: e has no type: "</span>
<a name="l00173"></a>00173 + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00174"></a>00174 <span class="keywordtype">bool</span> useIff = t.<a class="code" href="classCVC3_1_1Type.html#a38bba404056eadf3c283a67ab2347e02">isBool</a>();
<a name="l00175"></a>00175 <span class="keywordflow">if</span>(useIff)
<a name="l00176"></a>00176 pf = newPf(<span class="stringliteral">"rewrite_ite_else_iff"</span>, e, elseThm.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l00177"></a>00177 <span class="keywordflow">else</span> {
<a name="l00178"></a>00178 pf = newPf(<span class="stringliteral">"rewrite_ite_else"</span>, e, elseThm.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l00179"></a>00179 }
<a name="l00180"></a>00180 }
<a name="l00181"></a>00181 <span class="keywordflow">return</span> newRWTheorem(e, e[0].iteExpr(e[1], elseThm.<a class="code" href="classCVC3_1_1Theorem.html#a97d957fcbf9094480851b1d2e5d3729f">getRHS</a>()), a, pf);
<a name="l00182"></a>00182 }
<a name="l00183"></a>00183
<a name="l00184"></a>00184 <span class="comment">// ==> ITE(c, e1, e2) <=> (!c OR e1) AND (c OR e2)</span>
<a name="l00185"></a>00185 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00186"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#ac888377c574a056b251446902c010352">00186</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#ac888377c574a056b251446902c010352" title="==> ITE(c, e1, e2) <=> (c => e1) AND (!c => e2)">CoreTheoremProducer::rewriteIteBool</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& c,
<a name="l00187"></a>00187 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e2) {
<a name="l00188"></a>00188 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00189"></a>00189 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e1.<a class="code" href="group__ExprPkg.html#ga42929221eb172250697b72c28af6de07" title="Get the type. Recursively compute if necessary.">getType</a>().<a class="code" href="classCVC3_1_1Type.html#a38bba404056eadf3c283a67ab2347e02">isBool</a>() && e2.<a class="code" href="group__ExprPkg.html#ga42929221eb172250697b72c28af6de07" title="Get the type. Recursively compute if necessary.">getType</a>().<a class="code" href="classCVC3_1_1Type.html#a38bba404056eadf3c283a67ab2347e02">isBool</a>(),
<a name="l00190"></a>00190 <span class="stringliteral">"rewriteIteBool: Not a boolean ITE: "</span>
<a name="l00191"></a>00191 + c.<a class="code" href="group__ExprPkg.html#ga5532cabad6f699c57da32a8db65a38da">iteExpr</a>(e1, e2).<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00192"></a>00192 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00193"></a>00193 <span class="keywordflow">if</span>(withProof())
<a name="l00194"></a>00194 pf = newPf(<span class="stringliteral">"rewrite_ite_bool"</span>, c, e1, e2);
<a name="l00195"></a>00195 <span class="keywordflow">return</span> newRWTheorem(c.<a class="code" href="group__ExprPkg.html#ga5532cabad6f699c57da32a8db65a38da">iteExpr</a>(e1,e2),
<a name="l00196"></a>00196 (e1.<a class="code" href="group__ExprPkg.html#gaf310870d783fff343e77ba9c2277c626">orExpr</a>(!c).<a class="code" href="group__ExprPkg.html#ga6c3651465ce69ed5f4e6fd461b9acf3c">andExpr</a>(c.<a class="code" href="group__ExprPkg.html#gaf310870d783fff343e77ba9c2277c626">orExpr</a>(e2))), <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00197"></a>00197 }
<a name="l00198"></a>00198
<a name="l00199"></a>00199 <span class="comment"></span>
<a name="l00200"></a>00200 <span class="comment">//! |= (A & B1) | (A & B2) | ... | (A & bn) <=> A & (B1 | B2 | ...| Bn)</span>
<a name="l00201"></a>00201 <span class="comment"></span><a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00202"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a84abfb7cac1d339c43b322b097aa574c">00202</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a84abfb7cac1d339c43b322b097aa574c" title="|= (A & B1) | (A & B2) | ... | (A & bn) <=> A & (B1 | B2 | ...| Bn)">CoreTheoremProducer::orDistributivityRule</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l00203"></a>00203 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l00204"></a>00204 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#ga36f1eff876808586db368dc1b6da5f56">isOr</a>() && e.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() >= 2,
<a name="l00205"></a>00205 <span class="stringliteral">"CoreTheoremProducer::orDistributivityRule: "</span>
<a name="l00206"></a>00206 <span class="stringliteral">"input must be an OR expr: \n"</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00207"></a>00207 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e0 = e[0];
<a name="l00208"></a>00208
<a name="l00209"></a>00209 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e0.isAnd() && e0.arity() == 2,
<a name="l00210"></a>00210 <span class="stringliteral">"CoreTheoremProducer::orDistributivityRule: "</span>
<a name="l00211"></a>00211 <span class="stringliteral">"input must be an OR of binary ANDs: \n"</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00212"></a>00212 }
<a name="l00213"></a>00213
<a name="l00214"></a>00214 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& A = e[0][0];
<a name="l00215"></a>00215
<a name="l00216"></a>00216 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l00217"></a>00217 <span class="keywordflow">for</span>(<a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i=e.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>(),iend=e.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>();i!=iend;++i) {
<a name="l00218"></a>00218 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& ei = *i;
<a name="l00219"></a>00219 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(ei.<a class="code" href="group__ExprPkg.html#ga383260cf4f8919728e2712e6e11f21fa">isAnd</a>() && ei.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() == 2,
<a name="l00220"></a>00220 <span class="stringliteral">"CoreTheoremProducer::orDistributivityRule: "</span>
<a name="l00221"></a>00221 <span class="stringliteral">"input must be an OR of binary ANDs: \n"</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00222"></a>00222 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(A == ei[0],
<a name="l00223"></a>00223 <span class="stringliteral">"CoreTheoremProducer::orDistributivityRule: "</span>
<a name="l00224"></a>00224 <span class="stringliteral">"input must have a common factor: \n"</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00225"></a>00225 }
<a name="l00226"></a>00226 }
<a name="l00227"></a>00227 vector<Expr> output;
<a name="l00228"></a>00228 <span class="keywordflow">for</span>(<a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i=e.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>(),iend=e.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>();i!=iend;++i) {
<a name="l00229"></a>00229 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ei = *i;
<a name="l00230"></a>00230 output.push_back(ei[1]);
<a name="l00231"></a>00231 }
<a name="l00232"></a>00232 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> out = A.<a class="code" href="group__ExprPkg.html#ga6c3651465ce69ed5f4e6fd461b9acf3c">andExpr</a>(<a class="code" href="namespaceCVC3.html#a30f30b6e20c174f21ae63acea8618294">orExpr</a>(output));
<a name="l00233"></a>00233
<a name="l00234"></a>00234 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00235"></a>00235 <span class="keywordflow">if</span>(withProof())
<a name="l00236"></a>00236 pf = newPf(<span class="stringliteral">"or_distribuitivity_rule"</span>, e);
<a name="l00237"></a>00237
<a name="l00238"></a>00238 <span class="keywordflow">return</span> newRWTheorem(e, out, <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00239"></a>00239 }
<a name="l00240"></a>00240
<a name="l00241"></a>00241
<a name="l00242"></a>00242 <span class="comment"></span>
<a name="l00243"></a>00243 <span class="comment">//! |= (A | B1) & (A | B2) & ... & (A | bn) <=> A | (B1 & B2 & ...& Bn)</span>
<a name="l00244"></a>00244 <span class="comment"></span><a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00245"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#af5e5fb97e5fe6197e42c2c44e1757bb3">00245</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#af5e5fb97e5fe6197e42c2c44e1757bb3" title="|= (A | B1) & (A | B2) & ... & (A | bn) <=> A | (B1 & B2 & ...& Bn)">CoreTheoremProducer::andDistributivityRule</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l00246"></a>00246 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l00247"></a>00247 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#ga383260cf4f8919728e2712e6e11f21fa">isAnd</a>() && e.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() >= 2,
<a name="l00248"></a>00248 <span class="stringliteral">"CoreTheoremProducer::andDistributivityRule: "</span>
<a name="l00249"></a>00249 <span class="stringliteral">"input must be an AND expr: \n"</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00250"></a>00250 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e0 = e[0];
<a name="l00251"></a>00251
<a name="l00252"></a>00252 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e0.isOr() && e0.arity() == 2,
<a name="l00253"></a>00253 <span class="stringliteral">"CoreTheoremProducer::orDistributivityRule: "</span>
<a name="l00254"></a>00254 <span class="stringliteral">"input must be an AND of binary ORs: \n"</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00255"></a>00255 }
<a name="l00256"></a>00256
<a name="l00257"></a>00257 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& A = e[0][0];
<a name="l00258"></a>00258
<a name="l00259"></a>00259 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l00260"></a>00260 <span class="keywordflow">for</span>(<a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i=e.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>(),iend=e.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>();i!=iend;++i) {
<a name="l00261"></a>00261 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& ei = *i;
<a name="l00262"></a>00262 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(ei.<a class="code" href="group__ExprPkg.html#ga36f1eff876808586db368dc1b6da5f56">isOr</a>() && ei.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() == 2,
<a name="l00263"></a>00263 <span class="stringliteral">"CoreTheoremProducer::andDistributivityRule: "</span>
<a name="l00264"></a>00264 <span class="stringliteral">"input must be an AND of binary ORs: \n"</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00265"></a>00265 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(A == ei[0],
<a name="l00266"></a>00266 <span class="stringliteral">"CoreTheoremProducer::andDistributivityRule: "</span>
<a name="l00267"></a>00267 <span class="stringliteral">"input must have a common factor: \n"</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00268"></a>00268 }
<a name="l00269"></a>00269 }
<a name="l00270"></a>00270 vector<Expr> output;
<a name="l00271"></a>00271 <span class="keywordflow">for</span>(<a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i=e.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>(),iend=e.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>();i!=iend;++i) {
<a name="l00272"></a>00272 output.push_back((*i)[1]);
<a name="l00273"></a>00273 }
<a name="l00274"></a>00274 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> out = A.<a class="code" href="group__ExprPkg.html#gaf310870d783fff343e77ba9c2277c626">orExpr</a>(<a class="code" href="namespaceCVC3.html#ad4258158bba138eb54b9080af7f8223a">andExpr</a>(output));
<a name="l00275"></a>00275
<a name="l00276"></a>00276 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00277"></a>00277 <span class="keywordflow">if</span>(withProof())
<a name="l00278"></a>00278 pf = newPf(<span class="stringliteral">"and_distribuitivity_rule"</span>, e);
<a name="l00279"></a>00279
<a name="l00280"></a>00280 <span class="keywordflow">return</span> newRWTheorem(e, out, <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00281"></a>00281 }
<a name="l00282"></a>00282
<a name="l00283"></a>00283 <span class="comment">// ==> IMPLIES(e1,e2) IFF OR(!e1, e2)</span>
<a name="l00284"></a>00284 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00285"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#ac88efa4d7c591f187d3212c7162ef9a5">00285</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#ac88efa4d7c591f187d3212c7162ef9a5" title="==> IMPLIES(e1,e2) IFF OR(!e1, e2)">CoreTheoremProducer::rewriteImplies</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l00286"></a>00286 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00287"></a>00287 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00288"></a>00288 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#ga9067c706c6454ea1761ace7d7837af46">isImpl</a>(), <span class="stringliteral">"rewriteImplies precondition violated"</span>);
<a name="l00289"></a>00289 <span class="keywordflow">if</span>(withProof()) {
<a name="l00290"></a>00290 pf = newPf(<span class="stringliteral">"rewrite_implies"</span>, e[0], e[1]);
<a name="l00291"></a>00291 }
<a name="l00292"></a>00292 <span class="keywordflow">return</span> newRWTheorem(e, !e[0] || e[1], <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00293"></a>00293 }
<a name="l00294"></a>00294
<a name="l00295"></a>00295 <span class="comment">// ==> DISTINCT(e1,...,en) IFF AND 1 <= i < j <= n (e[i] /= e[j])</span>
<a name="l00296"></a>00296 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00297"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a17536e7c7ffa8d9a34981458a20f21ff">00297</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a17536e7c7ffa8d9a34981458a20f21ff" title="==> DISTINCT(e1,...,en) IFF AND 1 <= i < j <= n (e[i] /= e[j])">CoreTheoremProducer::rewriteDistinct</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l00298"></a>00298 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00299"></a>00299 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l00300"></a>00300 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5baa23a9880eca693f679c969556249925f">DISTINCT</a>, <span class="stringliteral">"rewriteDistinct precondition violated"</span>);
<a name="l00301"></a>00301 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() > 0, <span class="stringliteral">"rewriteDistinct precondition violated"</span>);
<a name="l00302"></a>00302 }
<a name="l00303"></a>00303 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> res;
<a name="l00304"></a>00304 <span class="keywordflow">if</span> (e.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() == 1) {
<a name="l00305"></a>00305 res = e.<a class="code" href="group__ExprPkg.html#gab57ce3dfa78947a906241d090c7cf34d">getEM</a>()-><a class="code" href="group__EM__Priv.html#ga4471fca49c2acbb7b4cf71e72bc55d6a" title="TRUE Expr.">trueExpr</a>();
<a name="l00306"></a>00306 }
<a name="l00307"></a>00307 <span class="keywordflow">else</span> <span class="keywordflow">if</span> (e.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() == 2) {
<a name="l00308"></a>00308 res = !(e[0].<a class="code" href="group__ExprPkg.html#gacb48495ca445c895f95d0c3c1ae2070b">eqExpr</a>(e[1]));
<a name="l00309"></a>00309 }
<a name="l00310"></a>00310 <span class="keywordflow">else</span> {
<a name="l00311"></a>00311 vector<Expr> tmp;
<a name="l00312"></a>00312 <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < e.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>(); ++i) {
<a name="l00313"></a>00313 <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i+1; j < e.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>(); ++j) {
<a name="l00314"></a>00314 tmp.push_back(!(e[i].eqExpr(e[j])));
<a name="l00315"></a>00315 }
<a name="l00316"></a>00316 }
<a name="l00317"></a>00317 res = <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>(<a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5ba865555c9f2e0458a7078486aa1b3254f">AND</a>, tmp);
<a name="l00318"></a>00318 }
<a name="l00319"></a>00319 <span class="keywordflow">if</span>(withProof()) {
<a name="l00320"></a>00320 pf = newPf(<span class="stringliteral">"rewrite_distinct"</span>, e , res);
<a name="l00321"></a>00321 }
<a name="l00322"></a>00322
<a name="l00323"></a>00323 <span class="keywordflow">return</span> newRWTheorem(e, res, <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00324"></a>00324 }
<a name="l00325"></a>00325
<a name="l00326"></a>00326 <span class="comment">// ==> NOT(e) == ITE(e, FALSE, TRUE)</span>
<a name="l00327"></a>00327 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00328"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a287bd6f15c149c66f1aea020cd144571">00328</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a287bd6f15c149c66f1aea020cd144571" title="==> NOT(e) == ITE(e, FALSE, TRUE)">CoreTheoremProducer::NotToIte</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& not_e){
<a name="l00329"></a>00329 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00330"></a>00330 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00331"></a>00331 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(not_e.<a class="code" href="group__ExprPkg.html#ga1a898858ccadce833df5a294c7740f11">isNot</a>() && not_e[0].<a class="code" href="group__ExprPkg.html#ga42929221eb172250697b72c28af6de07" title="Get the type. Recursively compute if necessary.">getType</a>().<a class="code" href="classCVC3_1_1Type.html#a38bba404056eadf3c283a67ab2347e02">isBool</a>(),
<a name="l00332"></a>00332 <span class="stringliteral">"NotToIte precondition violated"</span>);
<a name="l00333"></a>00333 <span class="keywordflow">if</span>(withProof())
<a name="l00334"></a>00334 pf = newPf(<span class="stringliteral">"NotToIte"</span>, not_e[0]);
<a name="l00335"></a>00335 <span class="keywordflow">if</span>(not_e[0].isTrue())
<a name="l00336"></a>00336 <span class="keywordflow">return</span> d_core->getCommonRules()->rewriteNotTrue(not_e);
<a name="l00337"></a>00337 <span class="keywordflow">else</span> <span class="keywordflow">if</span>(not_e[0].isFalse())
<a name="l00338"></a>00338 <span class="keywordflow">return</span> d_core->getCommonRules()->rewriteNotFalse(not_e);
<a name="l00339"></a>00339 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ite(not_e[0].iteExpr(d_em->falseExpr(), d_em->trueExpr()));
<a name="l00340"></a>00340 <span class="keywordflow">return</span> newRWTheorem(not_e, ite, <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00341"></a>00341 }
<a name="l00342"></a>00342
<a name="l00343"></a>00343 <span class="comment">// ==> Or(e) == ITE(e[1], TRUE, e[0])</span>
<a name="l00344"></a>00344 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00345"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a23a4580e5eb68d197db655776c5e8b0a">00345</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a23a4580e5eb68d197db655776c5e8b0a" title="==> Or(e) == ITE(e[1], TRUE, e[0])">CoreTheoremProducer::OrToIte</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e){
<a name="l00346"></a>00346 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00347"></a>00347 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#ga36f1eff876808586db368dc1b6da5f56">isOr</a>(),
<a name="l00348"></a>00348 <span class="stringliteral">"OrToIte: precondition violated: "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00349"></a>00349 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00350"></a>00350 <span class="keywordflow">if</span>(withProof()) {
<a name="l00351"></a>00351 pf = newPf(<span class="stringliteral">"OrToIte"</span>, e);
<a name="l00352"></a>00352 }
<a name="l00353"></a>00353 <span class="keyword">const</span> vector<Expr>& kids = e.<a class="code" href="group__ExprPkg.html#ga1e18ae89889e781591eb2874a4196b73">getKids</a>();
<a name="l00354"></a>00354 <span class="keywordtype">unsigned</span> k(kids.size());
<a name="l00355"></a>00355 <span class="keywordflow">if</span>(k==0)
<a name="l00356"></a>00356 <span class="keywordflow">return</span> newRWTheorem(e, d_em->falseExpr(), <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00357"></a>00357 <span class="keywordflow">if</span>(k==1)
<a name="l00358"></a>00358 <span class="keywordflow">return</span> newRWTheorem(e, e[0], <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00359"></a>00359 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ite(kids[k-1]);
<a name="l00360"></a>00360 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00361"></a>00361 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(!ite.<a class="code" href="group__ExprPkg.html#ga42929221eb172250697b72c28af6de07" title="Get the type. Recursively compute if necessary.">getType</a>().<a class="code" href="classCVC3_1_1Type.html#ab5fe00c99ee91f369e3339b26bab0bf7">isNull</a>(),
<a name="l00362"></a>00362 <span class="stringliteral">"OrToIte: kid "</span> + <a class="code" href="namespaceCVC3.html#af69618103f1f0f2eadada0796a2a940c">int2string</a>(k-1) + <span class="stringliteral">" has no type: "</span>
<a name="l00363"></a>00363 + (ite).toString());
<a name="l00364"></a>00364 <span class="keywordflow">for</span> (; k > 1; k--) {
<a name="l00365"></a>00365 <span class="keywordflow">if</span> (kids[k-2].isTrue()) {
<a name="l00366"></a>00366 ite = d_em->trueExpr();
<a name="l00367"></a>00367 <span class="keywordflow">break</span>;
<a name="l00368"></a>00368 }
<a name="l00369"></a>00369 <span class="keywordflow">else</span> <span class="keywordflow">if</span>(kids[k-2].isFalse()) <span class="keywordflow">continue</span>;
<a name="l00370"></a>00370 <span class="keywordflow">else</span>{
<a name="l00371"></a>00371 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00372"></a>00372 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(!kids[k-2].getType().isNull(),
<a name="l00373"></a>00373 <span class="stringliteral">"OrToIte: kid "</span> + <a class="code" href="namespaceCVC3.html#af69618103f1f0f2eadada0796a2a940c">int2string</a>(k-2) + <span class="stringliteral">" has no type: "</span>
<a name="l00374"></a>00374 + (kids[k-2]).toString());
<a name="l00375"></a>00375 ite = ite.<a class="code" href="group__ExprPkg.html#ga5532cabad6f699c57da32a8db65a38da">iteExpr</a>(d_em->trueExpr(), kids[k-2]);
<a name="l00376"></a>00376 }
<a name="l00377"></a>00377 }
<a name="l00378"></a>00378 <span class="keywordflow">return</span> newRWTheorem(e, ite, <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00379"></a>00379 }
<a name="l00380"></a>00380
<a name="l00381"></a>00381 <span class="comment">// ==> And(e) == ITE(e[1], e[0], FALSE)</span>
<a name="l00382"></a>00382 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00383"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#aaa435d07458188d1380e42d51c70b419">00383</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#aaa435d07458188d1380e42d51c70b419" title="==> And(e) == ITE(e[1], e[0], FALSE)">CoreTheoremProducer::AndToIte</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e){
<a name="l00384"></a>00384 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00385"></a>00385 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#ga383260cf4f8919728e2712e6e11f21fa">isAnd</a>(),
<a name="l00386"></a>00386 <span class="stringliteral">"AndToIte: precondition violated: "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00387"></a>00387 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00388"></a>00388 <span class="keywordflow">if</span>(withProof()) {
<a name="l00389"></a>00389 pf = newPf(<span class="stringliteral">"AndToIte"</span>, e);
<a name="l00390"></a>00390 }
<a name="l00391"></a>00391 <span class="keyword">const</span> vector<Expr>& kids = e.<a class="code" href="group__ExprPkg.html#ga1e18ae89889e781591eb2874a4196b73">getKids</a>();
<a name="l00392"></a>00392 <span class="keywordtype">unsigned</span> k(kids.size());
<a name="l00393"></a>00393 <span class="keywordflow">if</span>(k==0)
<a name="l00394"></a>00394 <span class="keywordflow">return</span> newRWTheorem(e, d_em->trueExpr(), <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00395"></a>00395 <span class="keywordflow">if</span>(k==1)
<a name="l00396"></a>00396 <span class="keywordflow">return</span> newRWTheorem(e, e[0], <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00397"></a>00397 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ite(kids[k-1]);
<a name="l00398"></a>00398 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00399"></a>00399 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(!ite.<a class="code" href="group__ExprPkg.html#ga42929221eb172250697b72c28af6de07" title="Get the type. Recursively compute if necessary.">getType</a>().<a class="code" href="classCVC3_1_1Type.html#ab5fe00c99ee91f369e3339b26bab0bf7">isNull</a>(),
<a name="l00400"></a>00400 <span class="stringliteral">"AndToIte: kid "</span> + <a class="code" href="namespaceCVC3.html#af69618103f1f0f2eadada0796a2a940c">int2string</a>(k-1) + <span class="stringliteral">" has no type: "</span>
<a name="l00401"></a>00401 + (ite).toString());
<a name="l00402"></a>00402 <span class="keywordflow">for</span> (; k > 1; k--) {
<a name="l00403"></a>00403 <span class="keywordflow">if</span> (kids[k-2].isFalse()) {
<a name="l00404"></a>00404 ite = d_em->falseExpr();
<a name="l00405"></a>00405 <span class="keywordflow">break</span>;
<a name="l00406"></a>00406 }
<a name="l00407"></a>00407 <span class="keywordflow">else</span> <span class="keywordflow">if</span>(kids[k-2].isTrue()) {
<a name="l00408"></a>00408 <span class="keywordflow">continue</span>;
<a name="l00409"></a>00409 }
<a name="l00410"></a>00410 <span class="keywordflow">else</span>{
<a name="l00411"></a>00411 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00412"></a>00412 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(!kids[k-2].getType().isNull(),
<a name="l00413"></a>00413 <span class="stringliteral">"AndToIte: kid "</span> + <a class="code" href="namespaceCVC3.html#af69618103f1f0f2eadada0796a2a940c">int2string</a>(k-2) + <span class="stringliteral">" has no type: "</span>
<a name="l00414"></a>00414 + (kids[k-2]).toString());
<a name="l00415"></a>00415 ite = ite.<a class="code" href="group__ExprPkg.html#ga5532cabad6f699c57da32a8db65a38da">iteExpr</a>(kids[k-2], d_em->falseExpr());
<a name="l00416"></a>00416 }
<a name="l00417"></a>00417 }
<a name="l00418"></a>00418 <span class="keywordflow">return</span> newRWTheorem(e, ite, <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00419"></a>00419 }
<a name="l00420"></a>00420
<a name="l00421"></a>00421 <span class="comment">// ==> IFF(a,b) == ITE(a, b, !b)</span>
<a name="l00422"></a>00422 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00423"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#af0a98459d73dbd5b89582d803f304aac">00423</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#af0a98459d73dbd5b89582d803f304aac" title="==> IFF(a,b) == ITE(a, b, !b)">CoreTheoremProducer::IffToIte</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e){
<a name="l00424"></a>00424 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00425"></a>00425 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#gabe385fb97505cccb75702378511c5375">isIff</a>() && e[0].<a class="code" href="group__ExprPkg.html#ga42929221eb172250697b72c28af6de07" title="Get the type. Recursively compute if necessary.">getType</a>().<a class="code" href="classCVC3_1_1Type.html#a38bba404056eadf3c283a67ab2347e02">isBool</a>() && e[1].<a class="code" href="group__ExprPkg.html#ga42929221eb172250697b72c28af6de07" title="Get the type. Recursively compute if necessary.">getType</a>().<a class="code" href="classCVC3_1_1Type.html#a38bba404056eadf3c283a67ab2347e02">isBool</a>(),
<a name="l00426"></a>00426 <span class="stringliteral">"IffToIte: precondition violated: "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00427"></a>00427 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00428"></a>00428 <span class="keywordflow">if</span>(e[0] == e[1]) <span class="keywordflow">return</span> d_core->getCommonRules()->reflexivityRule(e);
<a name="l00429"></a>00429 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ite(e[0].iteExpr(e[1], e[1].iteExpr(d_em->falseExpr(),
<a name="l00430"></a>00430 d_em->trueExpr())));
<a name="l00431"></a>00431 <span class="keywordflow">if</span>(withProof()) {
<a name="l00432"></a>00432 pf = newPf(<span class="stringliteral">"iff_to_ite"</span>, e);
<a name="l00433"></a>00433 }
<a name="l00434"></a>00434 <span class="keywordflow">return</span> newRWTheorem(e, ite, <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00435"></a>00435 }
<a name="l00436"></a>00436
<a name="l00437"></a>00437 <span class="comment">// ==> IMPLIES(a,b) == ITE(a, b, TRUE)</span>
<a name="l00438"></a>00438 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00439"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#aa5abdd3bfe669a3a0b28a92d28e8958a">00439</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#aa5abdd3bfe669a3a0b28a92d28e8958a" title="==> IMPLIES(a,b) == ITE(a, b, TRUE)">CoreTheoremProducer::ImpToIte</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e){
<a name="l00440"></a>00440 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00441"></a>00441 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#ga9067c706c6454ea1761ace7d7837af46">isImpl</a>() && e[0].<a class="code" href="group__ExprPkg.html#ga42929221eb172250697b72c28af6de07" title="Get the type. Recursively compute if necessary.">getType</a>().<a class="code" href="classCVC3_1_1Type.html#a38bba404056eadf3c283a67ab2347e02">isBool</a>() && e[1].<a class="code" href="group__ExprPkg.html#ga42929221eb172250697b72c28af6de07" title="Get the type. Recursively compute if necessary.">getType</a>().<a class="code" href="classCVC3_1_1Type.html#a38bba404056eadf3c283a67ab2347e02">isBool</a>(),
<a name="l00442"></a>00442 <span class="stringliteral">"ImpToIte: precondition violated: "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00443"></a>00443 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00444"></a>00444 <span class="keywordflow">if</span>(e[0] == e[1]) <span class="keywordflow">return</span> d_core->getCommonRules()->reflexivityRule(e);
<a name="l00445"></a>00445 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ite(e[0].iteExpr(e[1], d_em->trueExpr()));
<a name="l00446"></a>00446 <span class="keywordflow">if</span>(withProof()) {
<a name="l00447"></a>00447 pf = newPf(<span class="stringliteral">"imp_to_ite"</span>, e);
<a name="l00448"></a>00448 }
<a name="l00449"></a>00449 <span class="keywordflow">return</span> newRWTheorem(e, ite, <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00450"></a>00450 }
<a name="l00451"></a>00451
<a name="l00452"></a>00452
<a name="l00453"></a>00453 <span class="comment">// ==> ITE(e, FALSE, TRUE) IFF NOT(e)</span>
<a name="l00454"></a>00454 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00455"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a27d39117a5ede71d9c460b0232bdd469">00455</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a27d39117a5ede71d9c460b0232bdd469" title="==> ITE(e, FALSE, TRUE) IFF NOT(e)">CoreTheoremProducer::rewriteIteToNot</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e)
<a name="l00456"></a>00456 {
<a name="l00457"></a>00457 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00458"></a>00458 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#gaef13fa4752a1fb28e129a1efd0e26f01">isITE</a>() && e[1].<a class="code" href="group__ExprPkg.html#ga6173f64b22cba76472cd0c814bbf6dae">isFalse</a>() && e[2].<a class="code" href="group__ExprPkg.html#gadf8596df73fa69ff8e6a22b9321f5c34">isTrue</a>(),
<a name="l00459"></a>00459 <span class="stringliteral">"rewriteIteToNot: "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00460"></a>00460 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00461"></a>00461 <span class="keywordflow">if</span> (withProof()) pf = newPf(<span class="stringliteral">"rewrite_ite_to_not"</span>, e);
<a name="l00462"></a>00462 <span class="keywordflow">return</span> newRWTheorem(e, e[0].negate(), <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00463"></a>00463 }
<a name="l00464"></a>00464
<a name="l00465"></a>00465 <span class="comment">// ==> ITE(a, TRUE, b) IFF OR(a, b)</span>
<a name="l00466"></a>00466 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00467"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a2db95a382b0141d9a5098e9ca9ddd0f7">00467</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a2db95a382b0141d9a5098e9ca9ddd0f7" title="==> ITE(a, TRUE, b) IFF OR(a, b)">CoreTheoremProducer::rewriteIteToOr</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e)
<a name="l00468"></a>00468 {
<a name="l00469"></a>00469 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00470"></a>00470 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#gaef13fa4752a1fb28e129a1efd0e26f01">isITE</a>() && e[1].<a class="code" href="group__ExprPkg.html#gadf8596df73fa69ff8e6a22b9321f5c34">isTrue</a>(),
<a name="l00471"></a>00471 <span class="stringliteral">"rewriteIteToOr: "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00472"></a>00472 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00473"></a>00473 <span class="keywordflow">if</span> (withProof()) pf = newPf(<span class="stringliteral">"rewrite_ite_to_or"</span>, e);
<a name="l00474"></a>00474 <span class="keywordflow">return</span> newRWTheorem(e, e[0] || e[2], <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00475"></a>00475 }
<a name="l00476"></a>00476
<a name="l00477"></a>00477 <span class="comment">// ==> ITE(a, b, FALSE) IFF AND(a, b)</span>
<a name="l00478"></a>00478 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00479"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#ae681f89828ece60f9725c5696204cd72">00479</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#ae681f89828ece60f9725c5696204cd72" title="==> ITE(a, b, FALSE) IFF AND(a, b)">CoreTheoremProducer::rewriteIteToAnd</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e)
<a name="l00480"></a>00480 {
<a name="l00481"></a>00481 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00482"></a>00482 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#gaef13fa4752a1fb28e129a1efd0e26f01">isITE</a>() && e[2].<a class="code" href="group__ExprPkg.html#ga6173f64b22cba76472cd0c814bbf6dae">isFalse</a>(),
<a name="l00483"></a>00483 <span class="stringliteral">"rewriteIteToAnd: "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00484"></a>00484 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00485"></a>00485 <span class="keywordflow">if</span> (withProof()) pf = newPf(<span class="stringliteral">"rewrite_ite_to_and"</span>, e);
<a name="l00486"></a>00486 <span class="keywordflow">return</span> newRWTheorem(e, e[0] && e[1], <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00487"></a>00487 }
<a name="l00488"></a>00488
<a name="l00489"></a>00489 <span class="comment">// ==> ITE(a, b, !b) IFF IFF(a, b)</span>
<a name="l00490"></a>00490 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00491"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#abba61fa631a3e3fd6ae8761754f01c72">00491</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#abba61fa631a3e3fd6ae8761754f01c72" title="==> ITE(a, b, !b) IFF IFF(a, b)">CoreTheoremProducer::rewriteIteToIff</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e)
<a name="l00492"></a>00492 {
<a name="l00493"></a>00493 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00494"></a>00494 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#gaef13fa4752a1fb28e129a1efd0e26f01">isITE</a>() && e[1] == e[2].<a class="code" href="group__ExprPkg.html#gab1ce461dc931af73bf04e88c8d37dcbc">negate</a>(),
<a name="l00495"></a>00495 <span class="stringliteral">"rewriteIteToIff: "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00496"></a>00496 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00497"></a>00497 <span class="keywordflow">if</span> (withProof()) pf = newPf(<span class="stringliteral">"rewrite_ite_to_iff"</span>, e);
<a name="l00498"></a>00498 <span class="keywordflow">return</span> newRWTheorem(e, e[0].iffExpr(e[1]), <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00499"></a>00499 }
<a name="l00500"></a>00500
<a name="l00501"></a>00501 <span class="comment">// ==> ITE(a, b, TRUE) IFF IMPLIES(a, b)</span>
<a name="l00502"></a>00502 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00503"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#af0468c432ee5bfc5f82675f4b50e2002">00503</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#af0468c432ee5bfc5f82675f4b50e2002" title="==> ITE(a, b, TRUE) IFF IMPLIES(a, b)">CoreTheoremProducer::rewriteIteToImp</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e)
<a name="l00504"></a>00504 {
<a name="l00505"></a>00505 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00506"></a>00506 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#gaef13fa4752a1fb28e129a1efd0e26f01">isITE</a>() && e[2].<a class="code" href="group__ExprPkg.html#gadf8596df73fa69ff8e6a22b9321f5c34">isTrue</a>(),
<a name="l00507"></a>00507 <span class="stringliteral">"rewriteIteToImp: "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00508"></a>00508 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00509"></a>00509 <span class="keywordflow">if</span> (withProof()) pf = newPf(<span class="stringliteral">"rewrite_ite_to_imp"</span>, e);
<a name="l00510"></a>00510 <span class="keywordflow">return</span> newRWTheorem(e, e[0].impExpr(e[1]), <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00511"></a>00511 }
<a name="l00512"></a>00512
<a name="l00513"></a>00513
<a name="l00514"></a>00514 <span class="comment">// ==> ITE(a, b(a), c(a)) IFF ITE(a, b(TRUE), c(FALSE))</span>
<a name="l00515"></a>00515 <span class="comment">// ==> ITE(x = y, b, c) IFF ITE(x = y b[x/y], c[x = y/FALSE])</span>
<a name="l00516"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#acc27c290c53fdaab6977d43d765b10e3">00516</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#acc27c290c53fdaab6977d43d765b10e3" title="==> ITE(a, b(a), c(a)) IFF ITE(a, b(TRUE), c(FALSE))">CoreTheoremProducer::rewriteIteCond</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e)
<a name="l00517"></a>00517 {
<a name="l00518"></a>00518 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00519"></a>00519 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#gaef13fa4752a1fb28e129a1efd0e26f01">isITE</a>() && e.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>()==3, <span class="stringliteral">"rewriteIteCond: "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00520"></a>00520
<a name="l00521"></a>00521 vector<Expr> oldTerms, newTerms;
<a name="l00522"></a>00522 <span class="comment">// // if (e[0].isEq()) {</span>
<a name="l00523"></a>00523 <span class="comment">// // oldTerms.push_back(e[0][0]);</span>
<a name="l00524"></a>00524 <span class="comment">// // newTerms.push_back(e[0][1]);</span>
<a name="l00525"></a>00525 <span class="comment">// // }</span>
<a name="l00526"></a>00526 <span class="comment">// // else {</span>
<a name="l00527"></a>00527 oldTerms.push_back(e[0]);
<a name="l00528"></a>00528 newTerms.push_back(d_em->trueExpr());
<a name="l00529"></a>00529 <span class="comment">// }</span>
<a name="l00530"></a>00530
<a name="l00531"></a>00531 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> e1(e[1].substExpr(oldTerms, newTerms));
<a name="l00532"></a>00532 oldTerms[0] = e[0];
<a name="l00533"></a>00533 newTerms[0] = d_em->falseExpr();
<a name="l00534"></a>00534 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> e2(e[2].substExpr(oldTerms, newTerms));
<a name="l00535"></a>00535
<a name="l00536"></a>00536 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00537"></a>00537 <span class="keywordflow">if</span> (withProof()) pf = newPf(<span class="stringliteral">"rewrite_ite_cond"</span>, e);
<a name="l00538"></a>00538 <span class="keywordflow">return</span> newRWTheorem(e, e[0].iteExpr(e1, e2), <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00539"></a>00539 }
<a name="l00540"></a>00540
<a name="l00541"></a>00541
<a name="l00542"></a>00542 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00543"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a93299fd86567941880c6566e1d3af6b8">00543</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a93299fd86567941880c6566e1d3af6b8" title="((a|b)<=>(a|c))<=>(a|(b<=>c)); takes ((a|b)<=>(a|c)) as 'iff'">CoreTheoremProducer::iffOrDistrib</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& iff) {
<a name="l00544"></a>00544 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l00545"></a>00545 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(iff.<a class="code" href="group__ExprPkg.html#gabe385fb97505cccb75702378511c5375">isIff</a>() && iff.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>()==2, <span class="stringliteral">"iffOrDistrib("</span>
<a name="l00546"></a>00546 +iff.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">")"</span>);
<a name="l00547"></a>00547 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(iff[0].isOr() && iff[0].arity()==2, <span class="stringliteral">"iffOrDistrib("</span>
<a name="l00548"></a>00548 +iff.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">")"</span>);
<a name="l00549"></a>00549 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(iff[1].isOr() && iff[1].arity()==2, <span class="stringliteral">"iffOrDistrib("</span>
<a name="l00550"></a>00550 +iff.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">")"</span>);
<a name="l00551"></a>00551 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(iff[0][0]==iff[1][0], <span class="stringliteral">"iffOrDistrib("</span>
<a name="l00552"></a>00552 +iff.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">")"</span>);
<a name="l00553"></a>00553 }
<a name="l00554"></a>00554 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& a = iff[0][0];
<a name="l00555"></a>00555 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& b = iff[0][1];
<a name="l00556"></a>00556 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& c = iff[1][1];
<a name="l00557"></a>00557 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00558"></a>00558 <span class="keywordflow">if</span>(withProof())
<a name="l00559"></a>00559 pf = newPf(<span class="stringliteral">"iff_or_distrib"</span>, iff);
<a name="l00560"></a>00560 <span class="keywordflow">return</span> newRWTheorem(iff, (a || (b.<a class="code" href="group__ExprPkg.html#gaae017ca8e68af655ba285c985dd9fba5">iffExpr</a>(c))), <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00561"></a>00561 }
<a name="l00562"></a>00562
<a name="l00563"></a>00563
<a name="l00564"></a>00564 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00565"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#aecd467f33f9bcb736eadfa77f1a517aa">00565</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#aecd467f33f9bcb736eadfa77f1a517aa" title="((a&b)<=>(a&c))<=>(!a|(b<=>c)); takes ((a&b)<=>(a&c)) as 'iff'">CoreTheoremProducer::iffAndDistrib</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& iff) {
<a name="l00566"></a>00566 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l00567"></a>00567 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(iff.<a class="code" href="group__ExprPkg.html#gabe385fb97505cccb75702378511c5375">isIff</a>() && iff.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>()==2, <span class="stringliteral">"iffAndDistrib("</span>
<a name="l00568"></a>00568 +iff.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">")"</span>);
<a name="l00569"></a>00569 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(iff[0].isAnd() && iff[0].arity()==2, <span class="stringliteral">"iffAndDistrib("</span>
<a name="l00570"></a>00570 +iff.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">")"</span>);
<a name="l00571"></a>00571 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(iff[1].isAnd() && iff[1].arity()==2, <span class="stringliteral">"iffAndDistrib("</span>
<a name="l00572"></a>00572 +iff.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">")"</span>);
<a name="l00573"></a>00573 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(iff[0][0]==iff[1][0], <span class="stringliteral">"iffOrDistrib("</span>
<a name="l00574"></a>00574 +iff.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">")"</span>);
<a name="l00575"></a>00575 }
<a name="l00576"></a>00576 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& a = iff[0][0];
<a name="l00577"></a>00577 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& b = iff[0][1];
<a name="l00578"></a>00578 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& c = iff[1][1];
<a name="l00579"></a>00579 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00580"></a>00580 <span class="keywordflow">if</span>(withProof())
<a name="l00581"></a>00581 pf = newPf(<span class="stringliteral">"iff_and_distrib"</span>, iff);
<a name="l00582"></a>00582 <span class="keywordflow">return</span> newRWTheorem(iff, (!a || (b.<a class="code" href="group__ExprPkg.html#gaae017ca8e68af655ba285c985dd9fba5">iffExpr</a>(c))), <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00583"></a>00583 }
<a name="l00584"></a>00584
<a name="l00585"></a>00585
<a name="l00586"></a>00586 <span class="comment">// |- op(ITE(cond,a,b)) =/<=> ITE(cond,op(a),op(b))</span>
<a name="l00587"></a>00587 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00588"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#ac4ef57871856386e38e514d65e3b2c5e">00588</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#ac4ef57871856386e38e514d65e3b2c5e" title="|- op(ITE(cond,a,b)) =/<=> ITE(cond,op(a),op(b))">CoreTheoremProducer::ifLiftUnaryRule</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l00589"></a>00589 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l00590"></a>00590 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>()==1 && e[0].<a class="code" href="group__ExprPkg.html#gaef13fa4752a1fb28e129a1efd0e26f01">isITE</a>(),
<a name="l00591"></a>00591 <span class="stringliteral">"CoreTheoremProducer::ifLiftUnaryRule("</span>
<a name="l00592"></a>00592 <span class="stringliteral">"e = "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>() + <span class="stringliteral">")"</span>);
<a name="l00593"></a>00593 }
<a name="l00594"></a>00594 <a class="code" href="classCVC3_1_1Op.html">Op</a> op(e.<a class="code" href="group__ExprPkg.html#gace479f04faca399219496195152f7806" title="Get operator from expression.">getOp</a>());
<a name="l00595"></a>00595 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& ite = e[0];
<a name="l00596"></a>00596 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& cond = ite[0];
<a name="l00597"></a>00597 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& t1 = ite[1];
<a name="l00598"></a>00598 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& t2 = ite[2];
<a name="l00599"></a>00599
<a name="l00600"></a>00600 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l00601"></a>00601 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(cond.<a class="code" href="group__ExprPkg.html#ga42929221eb172250697b72c28af6de07" title="Get the type. Recursively compute if necessary.">getType</a>().<a class="code" href="classCVC3_1_1Type.html#a38bba404056eadf3c283a67ab2347e02">isBool</a>(),
<a name="l00602"></a>00602 <span class="stringliteral">"CoreTheoremProducer::ifLiftUnaryRule("</span>
<a name="l00603"></a>00603 <span class="stringliteral">"e = "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">")"</span>);
<a name="l00604"></a>00604 }
<a name="l00605"></a>00605
<a name="l00606"></a>00606 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> e1 = <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>(op, t1);
<a name="l00607"></a>00607 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> e2 = <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>(op, t2);
<a name="l00608"></a>00608
<a name="l00609"></a>00609 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> resultITE = cond.<a class="code" href="group__ExprPkg.html#ga5532cabad6f699c57da32a8db65a38da">iteExpr</a>(e1, e2);
<a name="l00610"></a>00610
<a name="l00611"></a>00611 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00612"></a>00612 <span class="keywordflow">if</span> (withProof())
<a name="l00613"></a>00613 pf = newPf(<span class="stringliteral">"if_lift_unary_rule"</span>, e);
<a name="l00614"></a>00614 <span class="keywordflow">return</span> newRWTheorem(e, resultITE, <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00615"></a>00615 }
<a name="l00616"></a>00616
<a name="l00617"></a>00617
<a name="l00618"></a>00618 <span class="comment">// (a & b) <=> a & b[a/true]; takes the index of a and rewrites all</span>
<a name="l00619"></a>00619 <span class="comment">// the other conjuncts.</span>
<a name="l00620"></a>00620 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00621"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a8c67942a0f72ee11abe27c992e0833c1">00621</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a8c67942a0f72ee11abe27c992e0833c1" title="(a & b) <=> a & b[a/true]; takes the index of a">CoreTheoremProducer::rewriteAndSubterms</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e, <span class="keywordtype">int</span> idx) {
<a name="l00622"></a>00622 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l00623"></a>00623 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#ga383260cf4f8919728e2712e6e11f21fa">isAnd</a>() && 0 <= idx && idx < e.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>(),
<a name="l00624"></a>00624 <span class="stringliteral">"rewriteAndSubterms("</span>+e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()
<a name="l00625"></a>00625 +<span class="stringliteral">", idx="</span>+<a class="code" href="namespaceCVC3.html#af69618103f1f0f2eadada0796a2a940c">int2string</a>(idx)
<a name="l00626"></a>00626 +<span class="stringliteral">"):\n Expected an AND and a valid index of a child"</span>);
<a name="l00627"></a>00627 }
<a name="l00628"></a>00628 vector<Expr> kids;
<a name="l00629"></a>00629 <a class="code" href="classCVC3_1_1ExprHashMap.html">ExprHashMap<Expr></a> subst;
<a name="l00630"></a>00630 subst.<a class="code" href="classCVC3_1_1ExprHashMap.html#a7fb3e24bb67239243212af626cc2f976">insert</a>(e[idx], d_em->trueExpr());
<a name="l00631"></a>00631 <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0, iend=e.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>(); i<iend; ++i) {
<a name="l00632"></a>00632 <span class="keywordflow">if</span>(i==idx)
<a name="l00633"></a>00633 kids.push_back(e[i]);
<a name="l00634"></a>00634 <span class="keywordflow">else</span>
<a name="l00635"></a>00635 kids.push_back(e[i].substExpr(subst));
<a name="l00636"></a>00636 }
<a name="l00637"></a>00637 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00638"></a>00638 <span class="keywordflow">if</span>(withProof())
<a name="l00639"></a>00639 pf = newPf(<span class="stringliteral">"rewrite_and_subterms"</span>, e, d_em->newRatExpr(idx));
<a name="l00640"></a>00640 <span class="keywordflow">return</span> newRWTheorem(e, <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>(e.<a class="code" href="group__ExprPkg.html#gace479f04faca399219496195152f7806" title="Get operator from expression.">getOp</a>(), kids), <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00641"></a>00641 }
<a name="l00642"></a>00642
<a name="l00643"></a>00643
<a name="l00644"></a>00644 <span class="comment">// (a | b) <=> a | b[a/false]; takes the index of a and rewrites all</span>
<a name="l00645"></a>00645 <span class="comment">// the other disjuncts.</span>
<a name="l00646"></a>00646 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00647"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#ae6b1fd56b11dbe24218cd2f5c74518c9">00647</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#ae6b1fd56b11dbe24218cd2f5c74518c9" title="(a | b) <=> a | b[a/false]; takes the index of a">CoreTheoremProducer::rewriteOrSubterms</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e, <span class="keywordtype">int</span> idx) {
<a name="l00648"></a>00648 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l00649"></a>00649 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#ga36f1eff876808586db368dc1b6da5f56">isOr</a>() && 0 <= idx && idx < e.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>(),
<a name="l00650"></a>00650 <span class="stringliteral">"rewriteOrSubterms("</span>+e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()
<a name="l00651"></a>00651 +<span class="stringliteral">", idx="</span>+<a class="code" href="namespaceCVC3.html#af69618103f1f0f2eadada0796a2a940c">int2string</a>(idx)
<a name="l00652"></a>00652 +<span class="stringliteral">"):\n Expected an OR and a valid index of a child"</span>);
<a name="l00653"></a>00653 }
<a name="l00654"></a>00654 vector<Expr> kids;
<a name="l00655"></a>00655 <a class="code" href="classCVC3_1_1ExprHashMap.html">ExprHashMap<Expr></a> subst;
<a name="l00656"></a>00656 subst.<a class="code" href="classCVC3_1_1ExprHashMap.html#a7fb3e24bb67239243212af626cc2f976">insert</a>(e[idx], d_em->falseExpr());
<a name="l00657"></a>00657 <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0, iend=e.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>(); i<iend; ++i) {
<a name="l00658"></a>00658 <span class="keywordflow">if</span>(i==idx)
<a name="l00659"></a>00659 kids.push_back(e[i]);
<a name="l00660"></a>00660 <span class="keywordflow">else</span>
<a name="l00661"></a>00661 kids.push_back(e[i].substExpr(subst));
<a name="l00662"></a>00662 }
<a name="l00663"></a>00663 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00664"></a>00664 <span class="keywordflow">if</span>(withProof())
<a name="l00665"></a>00665 pf = newPf(<span class="stringliteral">"rewrite_or_subterms"</span>, e, d_em->newRatExpr(idx));
<a name="l00666"></a>00666 <span class="keywordflow">return</span> newRWTheorem(e, <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>(e.<a class="code" href="group__ExprPkg.html#gace479f04faca399219496195152f7806" title="Get operator from expression.">getOp</a>(), kids), <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00667"></a>00667 }
<a name="l00668"></a>00668
<a name="l00669"></a>00669
<a name="l00670"></a><a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a1990709421517a01d824217eed8d1021">00670</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CoreTheoremProducer.html#a1990709421517a01d824217eed8d1021" title="Temporary cheat for building theorems.">CoreTheoremProducer::dummyTheorem</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e)
<a name="l00671"></a>00671 {
<a name="l00672"></a>00672 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00673"></a>00673 <span class="keywordflow">return</span> newTheorem(e, <a class="code" href="classCVC3_1_1Assumptions.html#af309a39e2e013cc62b6d94c5812ad86b">Assumptions::emptyAssump</a>(), pf);
<a name="l00674"></a>00674 }
</pre></div></div>
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